I was getting the dreaded Limited or No Connectivity Error Message recently when setting up a computer for a friend. Using a wired Ethernet connection to the wireless router worked fine, but I could not connected properly to the wifi connection I had set up.
It turned out that the problem was that the key number was not set correctly. This defaults to 1, but I had used 3 because for some reason the D-link wireless router would not let me changed the WEP key on the first key, so I ended up using key 3.
Once I set this in the wireless connection settings on the PC, it connected correctly and I no longer got the nasty Limited or No Connectivity Error Message.